You can use a mixer to record multiple tracks to your DAW, but as said originally you would need to have multiple channels not just stereo. The Behringer UFX1204 can record 12 channels @ 24bit to a USB 3.0 Memory stick or 12 separate streams to a DAW, you can record them clean or with mixer FX. There are lots or others also but not to USB stick.

https://www.sweetwater.com/store/detail/UFX1204

or 16 channels
https://www.sweetwater.com/store/detail/UFX1604